I was in a position to provide some talking points for my company’s upper-level math textbooks. It was written in the aftermath of customer-induced pique regarding how we sell ourselves. While it’s focused on my company, the core idea of a problem-first approach extends beyond what we do in particular.
Continue reading “Problem-First Thinking”Rolling Every Number on a Die
Thanks to Mikhail for posing this problem.
On average, how many rolls would it take to see every face on a particular die?
Continue reading “Rolling Every Number on a Die”2022 Blogmas Day 23 – Defensive Runs Saved and Defensive WAR
Hot on the heels of Ultimate Zone Rating is another tool with the same goal: measure a player’s defensive contributions in terms of runs saved. This other statistic, Defensive Runs Saved (DRS), doesn’t just have a better name, but in my experience is favored over UZR in most situations.
Continue reading “2022 Blogmas Day 23 – Defensive Runs Saved and Defensive WAR”2022 Blogmas Day 21 – Fielding Percentage and Range Factor
Leading into the home stretch, let’s discuss some defensive statistics. As a category, these represent recent innovations in baseball, as defense is the most dynamic aspect of the game. Players can change where they are positioned, which affects their ability to get to a ball. As we gather more data — ball speed off the bat and launch angle — we can better analyze defensive ability. But it’s still messy.
Continue reading “2022 Blogmas Day 21 – Fielding Percentage and Range Factor”2022 Blogmas Day 20 – Pitcher WAR
We’ve already addressed the concept behind WAR (Wins Above Replacement) in the abstract and for offensive players in particular. Today, we’ll consider how we quantify runs for pitchers and overview calculating their WAR.
Continue reading “2022 Blogmas Day 20 – Pitcher WAR”2022 Blogmas Day 19 – Leverage Index
Relief pitchers can enter the game in very different situations, and that should be accounted for when evaluating their performance. Coming in to clean up a 12-0 victory (or defeat) is different than coming in during a close, tense game with a lot on the line. We measure this disparity using Leverage Index (LI).
Continue reading “2022 Blogmas Day 19 – Leverage Index”2022 Blogmas Day 18 – Fixing ERA+ With a Minus
ERA+ is a funny, messy statistic. Unlike OPS+, it doesn’t tell us how much better a player is than the league: it instead tells us how much worse the league is than the player. This ignores our intuition and causes unnecessary confusion. Furthermore, it makes it harder to use as a tool for direct comparison: someone with a 200 ERA+ is not twice as good as someone with a 150 ERA+, while that would effectively be true with OPS+ (and similar offensive statistics.)
Continue reading “2022 Blogmas Day 18 – Fixing ERA+ With a Minus”2022 Blogmas Day 17 – Expected FIP
FIP is a cool, clever, and simple statistic to try and normalize how we work with ERA in a way that simply ignores defensive factors. However, we can ignore, or normalize for, at least one other factor to adjust the comparison.
Continue reading “2022 Blogmas Day 17 – Expected FIP”